Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Recursive Filtering for Stochastic Systems With Filter-and-Forward Successive Relays

In this paper,the recursive filtering problem is considered for stochastic systems over filter-and-forward successive relay(FFSR)networks.An FFSR is located between the sensor and the remote filter to forward the measurement.In the successive relay,two cooperative relay nodes are adopted to forward the signals alternatively,thereby existing switching characteristics and inter-relay interferences(IRI).Since the filter-and-forward scheme is employed,the signal received by the relay is retransmitted after it passes through a linear filter.The objective of the paper is to concurrently design optimal recursive filters for FFSR and stochastic systems against switching characteristics and IRI of relays.First,a uniform measurement model is proposed by analyzing the transmission mechanism of FFSR.Then,novel filter structures with switching parameters are constructed for both FFSR and stochastic systems.With the help of the inductive method,filtering error covariances are presented in the form of coupled difference equations.Next,the desired filter gain matrices are further obtained by minimizing the trace of filtering error covariances.Moreover,the stability performance of the filtering algorithm is analyzed where the uniform bound is guaranteed on the filtering error covariance.Finally,the effectiveness of the proposed filtering method over FFSR is verified by a three-order resistance-inductance-capacitance circuit system.

Partially-Observed Maximum Principle for Backward Stochastic Differential Delay Equations

Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is convex.The adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional spaces.Linear backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed rapidly.The corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].

Exponential Synchronization of Delayed Stochastic Complex Dynamical Networks via Hybrid Impulsive Control

Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics.

High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.

Logical stochastic resonance in a cross-bifurcation non-smooth system

This paper investigates logical stochastic resonance(LSR)in a cross-bifurcation non-smooth system driven by Gaussian colored noise.In this system,a bifurcation parameter triggers a transition between monostability,bistability and tristability.By using Novikov's theorem and the unified colored noise approximation method,the approximate Fokker-Planck equation is obtained.Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations.We simulate the logic operation of the system in the bistable and tristable regions respectively.We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter.Furthermore,it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region,since the tristable region is more sensitive to noise than the bistable one.

Computing large deviation prefactors of stochastic dynamical systems based on machine learning

We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous process.Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes.Machine learning models have become key players in automating brain tumor detection.Gradient descent methods are the mainstream algorithms for solving machine learning models.In this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor detection.Firstly,the smooth hinge loss is introduced to be used as the loss function of SVM.It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization.Secondly,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the model.Finally,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth SVM.Distributed computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of data.The DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core resources.Due to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence speed.From the perspective of loss reduction,DPGD converges faster than PGD.The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection.Frompre-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

A modified stochastic finite-fault method for estimating strong ground motion:Validation and application

We developed a modified stochastic finite-fault method for estimating strong ground motions.An adjustment to the dynamic corner frequency was introduced,which accounted for the effect of the location of the subfault relative to the hypocenter and rupture propagation direction,to account for the influence of the rupture propagation direction on the subfault dynamic corner frequency.By comparing the peak ground acceleration(PGA),pseudo-absolute response spectra acceleration(PSA,damping ratio of 5%),and duration,the results of the modified and existing methods were compared,demonstrating that our proposed adjustment to the dynamic corner frequency can accurately reflect the rupture directivity effect.We applied our modified method to simulate near-field strong motions within 150 km of the 2008 MW7.9 Wenchuan earthquake rupture.Our modified method performed well over a broad period range,particularly at 0.04-4 s.The total deviations of the stochastic finite-fault method(EXSIM)and the modified EXSIM were 0.1676 and 0.1494,respectively.The modified method can effectively account for the influence of the rupture propagation direction and provide more realistic ground motion estimations for earthquake disaster mitigation.

Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry

UAV-aided cellular networks,millimeter wave(mm-wave)communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G)and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs)and the UAV base stations(UBSs)coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point pro-´cess of type II(MPH-II),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR)gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs.

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance(NCSR) model is proposed by combining the Woods–Saxon(WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect.Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio(PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

Stochastic Gradient Compression for Federated Learning over Wireless Network

As a mature distributed machine learning paradigm,federated learning enables wireless edge devices to collaboratively train a shared AI-model by stochastic gradient descent(SGD).However,devices need to upload high-dimensional stochastic gradients to edge server in training,which cause severe communication bottleneck.To address this problem,we compress the communication by sparsifying and quantizing the stochastic gradients of edge devices.We first derive a closed form of the communication compression in terms of sparsification and quantization factors.Then,the convergence rate of this communicationcompressed system is analyzed and several insights are obtained.Finally,we formulate and deal with the quantization resource allocation problem for the goal of minimizing the convergence upper bound,under the constraint of multiple-access channel capacity.Simulations show that the proposed scheme outperforms the benchmarks.

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.